The Year 2000 actuarial model has several key assumptions. Among them, it is assumed that the house-price appreciation rate is 3 percent per year and the expected interest rate stays at 7.8
60
percent level for all future years. 61 It is important to test how sensitive the actuarial model results presented in the above section are to the assumed values of these two parameters. In addition, a simple stress test methodology is used to examine the performance of the current book of business. A stress test is a type of scenario analysis used to evaluate the financial strength of loan portfolios and corporations under adverse business conditions. Securities rating agencies are in the process of developing similar stress scenarios for pools of reverse mortgages as part of their rating criteria. 62 Specifically, the customized stress test methodology employed by this study emphasizes short-term fluctuations in annual house-price appreciation rates. Results from different scenarios can then be combined into an overall estimate by the technique of probabilistic weighting or averaging. This section documents the sensitivity testing and scenario stress tests we have conducted on the actuarial model results.63
Sensitivity Testing
Four expected interest rate values, namely 6.8 percent, 7.8 percent, 8.8 percent and 9.8 percent, were used in the tests. The expected interest rates represent average mortgage rates expected over the life of the loans. Three values of the annual house-price appreciation rate, namely 2 percent, 3 percent and 4 percent, were allowed in combination with each of four expected interest rate values. Other things being equal, higher expected interest rates will result in a larger amount of net expected liability because of the increase in automatic charges. A lower level of future house-price
appreciation rate will have a similar effect. The outstanding loan balance will exceed the house value earlier in the life of the loan. Thus, it is more likely that the sale of the house will not cover the outstanding balance at termination.
Results of the sensitivity testing are presented in matrix format and are reported in Exhibit 7-10 and Exhibit 7-11, for total and per loan estimates respectively. The estimates for the base case are printed in the darkest shading in the two exhibits. Any shading in the two exhibits highlights a positive net worth (or negative net liability) estimate, implying that the reserve plus future premiums will be adequate to cover future claims for this combination of house-price appreciation and expected interest rate values.
Major findings from the two exhibits can be summarized as follows:
61
Recall that the 7.8-percent interest rate is the median expected rate for all the HECM originations. It serves as a proxy for future note rate in the actuarial model.
62
For example, see Structured Finance: Reverse Mortgage Criteria (Standard & Poor’s, New York, NY: 1999). 63
This sensitivity analysis did not consider changes in HECM termination speeds. Certainly, if HECM loans terminate more slowly than assumed, expected losses may increase. An analysis of the HECM termination rate assumption is presented in Chapter 8.
• In general, the actuarial model results are quite sensitive to changes in the values of future house-price appreciation and expected interest rates. In other words, the net worth
estimates reported in Exhibits 7-8 and 7-9 rest critically on the assumed values of 3-percent annual house-price appreciation and 7.8 percent expected interest rate.
Exhibit 7-10
Actuarial Model Results of Sensitivity Testing:
Net Expected Liability, Total Estimates (In Millions of Dollars)
Future Expected Interest Rate
6.8% 7.8% 8.8% 9.8% F ut ur e H o u se - Pr ic e A p pr ec iat io n R at e 2% $20.6 $57.1 $107.9 $163.7 3% -$55.5 -$17.0 $35.2 $93.6
4% -$118.1 -$83.7 -$33.8 $24.4
Note: Shading reflects a negative net expected liability, or positive net worth.
Exhibit 7-11
Actuarial Model Results of Sensitivity Testing:
Net Expected Liability, Per Loan Estimates
Future Expected Interest Rate
6.8% 7.8% 8.8% 9.8% F ut ur e H o u se - Pr ic e A p pr ec iat io n R at e 2% $696 $1,928 $3,642 $5,521
3% -$1,871 -$570 $1,187 $3,157
4% -$3,983 -$2,824 -$1,139 $824
Note: Shading reflects a negative net expected liability, or positive net worth.
One reason that the 2000 actuarial model results are so similar to the 1995 model results is that both models assume the same expected interest rate and house-price appreciation rate.
• If the annual house-price appreciation rate is set at 2 percent (1 percentage point below the base case value) for all future years, this book of business will result in a positive net liability (i.e., negative net worth) for all interest rates tested. For example, with a 2 percent house- price appreciation rate and a 7.8-percent expected interest rate, the overall net worth estimate will drop by $74.1 million (or $2,498 per loan) from the base case level to a negative net worth of $57.1 million (or $1,928 per loan).
• Compared to the effect of the annual house-price appreciation rate, the actuarial model results appear to be relatively less sensitive to changes in expected interested rate values. For instance, if the house price appreciation rate stays constant at the base case value (3 percent) and expected interest is set at the 8.8 percent level (a 1-percentage point increase from the base case value) for all future years, the net worth estimate will only drop by $52.2 million (or $1,757 per loan) from the base case level to a negative net worth of $35.2 million (or $1,187 per loan).
Stress Tests
Future events are uncertain. It is, however, quite unlikely that expected interest rates and house- price appreciation rates will stay abnormally high or low for all future years, as we assumed in the sensitivity testing above. Instead, from a policy-maker’s view point, it is more relevant to test how
short-term fluctuations in macroeconomic conditions, particularly changes in house-price
appreciation rates, will affect the performance of the current book of business in terms of expected net worth. This type of simulation is called scenario stress testing in the literature and is considered a powerful management tool in the industry.64 Specifically, three scenarios are considered here:
• Base case scenario. Macroeconomic conditions follow the assumed values in the actuarial model. In particular, the house-price appreciation rate will be 3 percent per year, and expected interest rate stays at 7.8 percent for all future years.
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• Alternative scenario #1. Let us assume that overall house prices fall at a rate of 2 percent per year for the next three years, due to economic shocks. That is, the house-price
appreciate rate is -2 percent for the next three years (5 percentage point lower than the value assumed in the Base Case Scenario). This can happen if the economy falls into recession. We assume the house-price appreciation will revert to the annual rate of 3 percent in the fourth year and beyond. Future expected interest rates stay constant at 7.8 percent for the entire scenario.
• Alternative scenario #2. Overall house-price appreciation soars at the rate of 8 percent per year for three years, due to high housing demand in a booming economy. That is, the house-price appreciation rate is 5 percentage points above the value assumed in the Base Case Scenario for the first three years. We assume the house-price appreciation will return to the annual rate of 3 percent right after that. Future expected interest rates stay constant at 7.8 percent for the entire scenario.
Results from the scenario stress tests are presented in Exhibit 7-12. They can be summarized as follows:
• For the Base Case, the net expected liability is -$17.0 million, or -$570 on a per loan basis, exactly as those reported in Exhibits 7-8 and 7-9.
• Alternative Scenario #1 results in a net expected liability of $72.9 million (or an average of $2,460 per loan) for the current book of business. This means that the reserve plus future premiums are not sufficient to cover future claims on the insurance fund. The implication is that a significant drop in property values, even for a relatively short period of time, can result in a sizable amount of negative net worth.
• For Alternative Scenario #2, the short-term and sharp increase in house prices yields an overall net expected liability of -$80.2 million (or -$2,704 per loan), implying that reserve plus future premiums will be more than enough to cover future claims.
• The simulation results of these two scenarios demonstrate the potential impact of regional heterogeneity of the HECM loans in this book of business. Although the house-price appreciation rates in the two alternative scenarios deviate from the Base Case in a
symmetric manner, the resulting changes in net worth are not symmetric. The net worth of Alternative Scenario #1 declines from the Base Case by about $90 million, whereas Alternative Scenario #2 yields a net worth that is only $63 million above the Base Case value. This is probably due to the fact that loan characteristics such as appraised values and outstanding balances are not distributed uniformly across the country. Even if the national average house-price appreciation rate remains unchanged, an increase in regional dispersion can have a harmful effect on the insurance fund reserves.
• Future events are uncertain. One way to combine the results from the three scenarios into a single stress-test estimate is to assign probabilities (or weights) to the events and, from that,
we can compute the expected (or weighted average) net worth estimate across the three scenarios. For example, we can assume that the three scenarios are equally likely to happen in the future, which implies that each gets the equal weight of 1/3. This will yield a weighted net worth of $8.1 million, or $272 per loan, for this book of business. Assigning the weights in a more rigorous manner is beyond the scope of this study.
Exhibit 7-12
Actuarial Model Results of the Stress Tests: Net Expected Liability
Assumptions Net Expected Liability
Total
(in millions)
Per Loan
Base Case Scenario
Future House-Price Appreciation Rate = 3%.
Future Expected Interest Rate = 7.8%.
-$17.0 -$570
Alternative Scenario #1
Future House-Price Appreciation Rate = - 2% for the next 3 years and then 3% for the rest. Future Expected Interest Rate = 7.8%.
$72.9 $2,460
Alternative Scenario #2
Future House-Price Appreciation Rate = 8% for the next 3 years and then 3% for the rest. Future Expected Interest Rate = 7.8%.